On a singularly perturbed initial value problem in the case of a double root of the degenerate equation
We study the initial value problem of a singularly perturbed first order ordinary differential equation in case that the degenerate equation has a double root. We construct the formal asymptotic expansion of the solution such that the boundary layer functions decay exponentially. This requires a mod...
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| Veröffentlicht in: | Nonlinear analysis 2013-05, Vol.83, p.1-11 |
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| container_title | Nonlinear analysis |
| container_volume | 83 |
| creator | Butuzov, V.F. Nefedov, N.N. Recke, L. Schneider, K.R. |
| description | We study the initial value problem of a singularly perturbed first order ordinary differential equation in case that the degenerate equation has a double root. We construct the formal asymptotic expansion of the solution such that the boundary layer functions decay exponentially. This requires a modification of the standard procedure. The asymptotic solution will be used to construct lower and upper solutions guaranteeing the existence of a unique solution and justifying its asymptotic expansion. |
| doi_str_mv | 10.1016/j.na.2013.01.013 |
| format | Article |
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| ispartof | Nonlinear analysis, 2013-05, Vol.83, p.1-11 |
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| language | eng |
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| source | Access via ScienceDirect (Elsevier) |
| subjects | Asymptotic expansion Asymptotic expansions Asymptotic properties Boundary layer Construction Decay Differential equations Double root of degenerate equation Initial value problem Initial value problems Mathematical analysis Roots Singularly perturbed first order ordinary differential equation |
| title | On a singularly perturbed initial value problem in the case of a double root of the degenerate equation |
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